What is the extreme x^4-50x^2+625 ?

The extreme x^4-50x^2+625 is Minimum(-5,0),Maximum(0,625),Minimum(5,0)

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extreme x^4-50x^2+625

extreme points

x^{4} - 50 x^{2} + 625

Minimum (- 5, 0), Maximum (0, 625), Minimum (5, 0)

Solution steps

f^{'} (x) = 4 x^{3} - 100 x

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

x^{4} - 50 x^{2} + 625 : 0

Minimum (- 5, 0)

Plug

x = 0

into

x^{4} - 50 x^{2} + 625 : 625

Maximum (0, 625)

Plug

x = 5

into

x^{4} - 50 x^{2} + 625 : 0

Minimum (5, 0)

Minimum (- 5, 0), Maximum (0, 625), Minimum (5, 0)

x - 12

f (x) = y + 3 = 2^{x}

(\frac{1}{2})^{x + 3}

x + 1 - 2 x

f (x) = \frac{( x - 1 ) ^{2}}{x ^{3} - 2 x ^{2} + x}

What is the extreme x^4-50x^2+625 ?
The extreme x^4-50x^2+625 is Minimum(-5,0),Maximum(0,625),Minimum(5,0)